Minimum Spanning Tree: Prim’s Algorithm

April 9, 2010

In the previous exercise we studied Kruskal’s algorithm for computing the minimum spanning tree of a weighted graph. Today we study an algorithm developed in 1930 by the Czech mathematician Vojtěch Jarník and rediscovered by Robert Prim in 1957.

Kruskal’s algorithm works by creating a singleton tree for each vertex and merging the trees by taking at each step the minimum-weight edge that joins two trees. Prim’s algorithm is the opposite; it starts with a single vertex and repeatedly joins the minimum-weight edge that joins the tree to a non-tree vertex. At each step the tree is a minimum spanning tree of the vertices that have been processed thus far.

Your task is to write a program to find the minimum spanning tree of a graph using Prim’s algorithm. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.